svd_tutorial.cpp
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00001 /*
00002  *    This file is part of ACADO Toolkit.
00003  *
00004  *    ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
00005  *    Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau,
00006  *    Milan Vukov, Rien Quirynen, KU Leuven.
00007  *    Developed within the Optimization in Engineering Center (OPTEC)
00008  *    under supervision of Moritz Diehl. All rights reserved.
00009  *
00010  *    ACADO Toolkit is free software; you can redistribute it and/or
00011  *    modify it under the terms of the GNU Lesser General Public
00012  *    License as published by the Free Software Foundation; either
00013  *    version 3 of the License, or (at your option) any later version.
00014  *
00015  *    ACADO Toolkit is distributed in the hope that it will be useful,
00016  *    but WITHOUT ANY WARRANTY; without even the implied warranty of
00017  *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00018  *    Lesser General Public License for more details.
00019  *
00020  *    You should have received a copy of the GNU Lesser General Public
00021  *    License along with ACADO Toolkit; if not, write to the Free Software
00022  *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
00023  *
00024  */
00025 
00026 
00027 
00039 #include <acado/utils/acado_utils.hpp>
00040 #include <acado/matrix_vector/matrix_vector.hpp>
00041 
00042 using namespace std;
00043 using namespace Eigen;
00044 
00045 USING_NAMESPACE_ACADO
00046 
00047 /* >>> start tutorial code >>> */
00048 int main( ){
00049 
00050 
00051 
00052     // DEFINE A MATRIX:
00053     // ----------------
00054     DMatrix A(3,2);
00055 
00056     A(0,0) = 1.0;  A(0,1) = 0.0;
00057     A(1,0) = 0.0;  A(1,1) = 3.0;
00058     A(2,0) = 0.0;  A(2,1) = 2.0;
00059 
00060 
00061 //  ----------------------------------------------
00062 //  Compute the singular value decomposition of A:
00063 //
00064 //               A = U D V^T
00065 //
00066 //  where U and V are orthogonal and D a diagonal
00067 //  matrix.
00068 //  ----------------------------------------------
00069 
00070     JacobiSVD< MatrixXd > svdA(A, ComputeThinU | ComputeThinV );
00071 
00072     DMatrix U = svdA.matrixU();
00073     DMatrix V = svdA.matrixV();
00074     DVector D = svdA.singularValues();
00075 
00076     cout << "U = " << endl << U << endl;
00077     cout << "D = " << endl << D << endl;
00078     cout << "V = " << endl << V << endl;
00079 
00080 
00081     // DEFINE ANOTHER MATRIX:
00082     // ----------------------
00083     DMatrix B(2,3);
00084 
00085     B(0,0) = 1.0;   B(0,1) = 0.0;  B(0,2) = 0.0;
00086     B(1,0) = 0.0;   B(1,1) = 3.0;  B(1,2) = 2.0;
00087 
00088 
00089 //  ----------------------------------------------
00090 //  Compute the singular value decomposition of B:
00091 //
00092 //               B = U D V^T
00093 //
00094 //  where U and V are orthogonal and D a diagonal
00095 //  matrix.
00096 //  ----------------------------------------------
00097 
00098     JacobiSVD< MatrixXd > svdB(B, ComputeThinU | ComputeThinV);
00099 
00100     U = svdB.matrixU();
00101     V = svdB.matrixV();
00102     D = svdB.singularValues();
00103 
00104     cout << "\n\nSVD of the matrix B: \n";
00105 
00106     cout << "U = " << endl << U << endl;
00107     cout << "D = " << endl << D << endl;
00108     cout << "V = " << endl << V << endl;
00109 
00110     return 0;
00111 }
00112 /* <<< end tutorial code <<< */
00113 
00114 


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Thu Aug 27 2015 12:01:10